Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Supersonic — where it appears

Moving faster than the speed at which pressure information travels, so that nothing downstream can inform anything upstream. The governing equations are hyperbolic, disturbances are confined to wedges, and a closed body has drag in the absence of any viscosity.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The wall is what cancels the waves it made. The characteristic net of a minimum-length nozzle designed for Mach 2.4, with 18 waves. The pale lines run from the sharp throat down to the axis, reflect there by symmetry, and run back up to the wall; the wall turns through exactly the angle needed to cancel each one as it arrives, so nothing reflects back into the flow and the exit is uniform at Mach 2.400 and parallel to 0.0 degrees. The area ratio decides the Mach number and this net decides the shape, and the two agree on the exit height to 0.51 per cent at this resolution.

The wall that cancels its own waves

The area ratio of a supersonic nozzle fixes its exit Mach number and says nothing whatever about its shape. What fixes the shape is a wave-by-wave construction in which the wall turns through exactly the angle needed to absorb each expansion as it arrives — and getting it wrong leaves a stream full of oblique shocks at precisely the right Mach number.

compressible · Characteristics Three aircraft, and the only thing the drag can see. The cross-sectional area against station, for a clean body, the same body with a wing added, and the body cut away where the wing is. The wave drag depends on this curve and on nothing else about the three shapes — so the middle one pays for its lump and the third does not, although the third has the same wing.

The drag that can only see one curve

A slender body's far field is a line of sources of strength A′(x), and nothing else about its shape reaches it. So its supersonic wave drag depends on the cross-sectional area distribution alone — and a fuselage cut away where the wing joins it can carry the wing for nothing.

inviscid · Slender body Zero wave drag at one Mach number, inside a loop it cannot enter from below. The wave drag of the pair, per unit of one element's chord, against Mach number, beside a single diamond of the pair's combined thickness. The biplane's drag is zero at its design Mach number, 1.944, and rises either side. Shaded: below 1.6 the channel cannot pass the flow at all; between 1.6 and 2.15 it can, but only if it was started above the band. Accelerating from subsonic, the biplane stays choked until Mach 2.15, past its design point.

Busemann's biplane has to be flown past its design point

Two half-diamonds facing across a channel cancel each other's waves at one Mach number and carry their thickness at no wave drag. The cancellation needs the channel narrowed at its middle, and a narrowed supersonic channel will not swallow the shock that forms in it on the way up. A biplane 3 per cent thick per element, designed for Mach 1.94, stays choked until Mach 2.15, and only one that is thinner than about 2.6 per cent can start by itself at any speed.

compressible · Wave drag

Named alongside it

The objects these essays reach for when they reach for this one.

Model limitArea machWave dragArea ruleChokingDimensionlessDiscretisationExpansion fanFar fieldHysteresisInterferenceInviscid

All concepts